Problem

Source: Taiwan 2nd TST 2005, 3rd independent study, problem 2

Tags: geometry, geometry solved



A quadrilateral PQRS has an inscribed circle, the points of tangencies with sides PQ, QR, RS, SP being A, B, C, D, respectively. Let the midpoints of AB, BC, CD, DA be E, F, G, H, respectively. Prove that the angle between segments PR and QS is equal to the angle between segments EG and FH.